Inductive sensors are typically based on a change in one or more characteristic values of a system of one or more inductive devices as a result of a measured variable. Inductive devices of this kind can refer to a coil, winding or inductance, for example.
Possible characteristic values are, in particular:                self inductance L, also called inductance for short,        resistance loss R, which is made up of a nonreactive resistance of the winding and other loss contributions,        complex impedance Z=jωL+R with the imaginary unit j and the angular frequency ω,        loss angle δ=arctan(Re{Z}/Im{Z}),        and, particularly in the case of the magnetic coupling between multiple devices, mutual inductance M. The mutual inductance M can be measured indirectly as an induced voltage in one conductor in reaction to a known current in another conductor, inter alia.        
Measured variables that bring about the change in the characteristics values may be position or length, angle, force, pressure or torque, inter alia. An application that can be cited by way of example is a position sensor for the brake pedal of an automobile.
For inductive sensors, there are particularly two main approaches to circuitry that exist in the prior art in order to perform electrical measurement of the characteristic values:
First, this is a resonant system: The inductive sensor with its variable characteristic value, more often than not of the inductance L, is part of the frequency-determining network of an oscillator. The oscillator always oscillates at its natural frequency, the most important influencing factor of which is L. The measurement of L is therefore committed to a frequency measurement that can easily be performed e.g. by counting the periods or zero crossings of the oscillator oscillation.
Second, this is a lock-in amplifier (also phase-sensitive rectifier, synchronous demodulator or carrier frequency amplifier): The inductive sensor is provided with a stimulus at a fixed frequency (current or voltage). A signal processing circuit measures the respective other electrical variable using the impedance (voltage or current). The signal processing is consistent with narrowband filtering of this variable around the frequency of the stimulus with subsequent determination of the complex amplitude and quotient formation with the stimulus to determine the characteristic value. These functions can be realised either using analog electronics or largely using the means of digital signal processing and software.
The two approaches have different disadvantages.
The resonant system has limitations for the conception of the inductive system, because only one oscillation per oscillator is possible. Multiple signals can be obtained only using multiple independent oscillators and inductive systems, which significantly increases the outlay for sensors with ratiometric or differential measurement. Furthermore, the inductive system always has frequency dependencies, i.e. it can only be designed in optimum fashion for one frequency; the frequency range of the oscillator is always a compromise. Via the alteration of the oscillation frequency, cross-sensitivities can corrupt the measurement result, for example because the inductance L in addition to the sensitivity to the measured variable is influenced by a further frequency-dependent variable. Finally, the difference between the maximum and minimum count results of the frequency measurement must exceed a minimum value for the respective demands on measurement accuracy and measurement resolution to be met. This requires a minimum measurement time, depending on frequency, that is sometimes not available at all.
The lock-in amplifier, by contrast, operates at a constant frequency, but also requires a stimulus at this frequency. The frequency of these enforced oscillations is freely selectable, but the frequency dependency of the inductive system means that this is an inconsistency for operation at resonance, i.e. with oscillations at the natural frequency. It is thus not possible for the following advantages of resonance to be used: The inductive system, operated as a resonator, is already a filter by virtue of its being able to achieve at its natural frequency a particularly high amplitude that facilitates the measurement. Interference whose frequency differs significantly from this frequency is rejected by the filter action. Furthermore, the power requirement of the inductive system to maintain the oscillation is at its lowest at resonance if all other parameters remain the same. For a given power of the stimulus, a particularly high amplitude is therefore possible. These two advantages are naturally the same substantive matter, once from the point of view of the measurement and once from the point of view of the stimulus.